Bring a large pot of water (salted) to a boil over high heat.
Wash the broccolini and trim off the rough end. Separate the stalks and the florets. Add the stalks to the boiling water and blanch for 1 minute. Then, add the florets and blanch everything for 1 more minute. Using a slotted spoon, transfer the broccolini to a large plate to cool. Keep the pot of water boiling.
Cook the pasta in the boiling water until tender but still firm to the bite, stirring occasionally. Reserve 1 cup of pasta water. Drain pasta. Set aside.
Meanwhile, cut the sausage lengthwise. Remove the casings of the sausage. Crumble the sausage into ½-inch pieces by hands. Transfer to a small bowl.
Once the broccolini are cool enough to handle, place them on a chopping board. Cut the florets into 1-inch long pieces. If the stalks are a bit thick, cut them into thinner pieces, then cut into 1-inch long as well.
In a Dutch oven or large skillet over medium heat, warm 1½ tablespoons olive oil (use only ½ tablespoons for Italian sausages). Add the sausage pieces and break them up even more with a wooden spatula. Cook until golden brown. (If using Italian sausages, you may want to use some paper towels to absorb some of the fat.)
Add garlic and red pepper flakes. Add 1/3 cup pasta water. Let it cook for 2 minutes. Add the chopped brocollini and butter. If it starts to dry out, add a bit more pasta water. Cook for 2 minutes.
Turn the heat down to medium-low. Add cooked pasta. Stir everything together and cook for 2 more minutes. Add lemon zest and lemon juice. Add more pasta water if needed. Toss in Parmesan cheese. Taste and adjust with salt and pepper. Transfer to serving plates. Top with extra Parmesan if desired. Serve immediately.